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Apple rolled back privacy rules Thursday that developers of apps for children had said would hurt their ability to make money and improve their products.

The rules, which were originally announced at Apple’s Worldwide Developers Conference in June, would have banned apps marketed to children from using external analytics software that collects detailed information about who is using the app and would have barred the apps from displaying ads.

Phil Schiller, Apple’s senior vice president of worldwide marketing, said the changes were the result of complaints from parents, but the restrictions set off an outcry among developers who defended their use of analytics as benign and said advertising services already vet ads for appropriateness.

Following an inquiry from The Washington Post last month, Apple delayed the rule changes pending discussions with developers.

On Thursday, Apple amended those rules to allow kids app developers to use analytics software “in limited cases,” provided the services don’t collect or transmit personally identifiable information about children or data that could be combined with data from other sources to identify them later.

Under the revised rules, advertising will be allowed, as long as it has been vetted for appropriateness.